Rewrite the function by completing the square. h(x)= 4 x^{2} -36 x +81

Answers

Answer 1

Answer:

4(x-4.5)^2

Step-by-step explanation:

h(x)=4x^2-36x+81

=4(x^2-9x)+81

=4(x^2-9x+20.25)-(4)(20.25)+81

=4(x-4.5)^2


Related Questions

A ball is thrown straight up from a cliff. The function f(x)= -4.9t^ + 17t +19 describes the height of the ball, in meters, as a function of time, t, in seconds. What is the maximum height of the ball? At what time is the height reached? Round your answer to one decimal place.

Answers

Answer:

  33.7 m at 1.7 seconds

Step-by-step explanation:

For quadratic ax^2+bx+c, the line of symmetry (x-coordinate of the vertex) is ...

  -b/(2a)

For your quadratic, the vertex (highest point) is reached at time ...

  t = -(17)/(2(-4.9)) = 17/9.8 ≈ 1.7 . . . . seconds

__

The height at that time is ...

  f(17/9.8) = (-4.9(17/9.8) +17)(17/9.8) +19 = 289/19.6 +19 ≈ 33.7 . . . meters

_____

Comment on the function evaluation

We have used the "Horner form" of the function to make evaluation easier.

  f(t) = (-4.9t +17)t +19

simplify the expression (3k / 8)^2​

Answers

Answer:

9k/64^2 (9k^2/64^2)

Step-by-step explanation:

Answer:

9k^2/64

Step-by-step explanation:

3*3=9

k*k=k^2

8*8=64

I really need some HELP.............

Answers

Answer:

119000

Step-by-step explanation:

The median is the middle value when placed from smallest to largest

95000, 112000, 126000, 13000

The middle is between 112000 and 126000 so take the average

(112000+126000)/2 =238000/2 =119000

Employees at a manufacturing plant have seen production
rates change by approximately 105% annually. In contrast,
the graph shows the change in the average annual wages
of the employees
Which statement accurately compares the annual change
in production to the annual change in average salary?
50.000
50.000
0 The annual changes cannot be compared because the
initial production value is unknown.
The annual change in production will, at some point,
exceed the annual change in average salary
The annual change in production increases at a slower
rate, 5% per year, than the annual increase in the
average salary, $500 per year.
The annual change in production increases at a slower
rate, 105% per year, than the annual increase in average
salary, $500 per year
40
30.000
20.000
10.000

Answers

Answer:

both measures show strong growth in CEO

Step-by-step explanation:

350 firms in 2018 was $17.2 million- or $14.0 both show that they have a strong growth in the last  2 years.

Answer:

The answer is B "The annual change in production has exceeded the annual change in the average salary."

Step-by-step explanation:

Yes

Gibbs Baby Food Company wishes to compare the weight gain of infants using its brand versus its competitor’s. A sample of 40 babies using the Gibbs products revealed a mean weight gain of 7.6 pounds in the first three months after birth. For the Gibbs brand, the population standard deviation of the sample is 2.3 pounds. A sample of 55 babies using the competitor’s brand revealed a mean increase in weight of 8.1 pounds. The population standard deviation is 2.9 pounds. At the .05 significance level, can we con- clude that babies using the Gibbs brand gained less weight? Compute the p-value and interpret it.

Answers

Answer:

[tex]z=\frac{(7.6-8.1)-0}{\sqrt{\frac{2.3^2}{40}+\frac{2.9^2}{55}}}}=-0.936[/tex]  

The p value can be founded with this formula:

[tex]p_v =P(z<-0.936)=0.175[/tex]  

Since the p value is higher than the significance level provided of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean for the Gibbs brand is significantly lower than the true mean for the competitor

Step-by-step explanation:

Information given

[tex]\bar X_{1}=7.6[/tex] represent the mean for Gibbs products

[tex]\bar X_{2}=8.1[/tex] represent the mean for the competitor

[tex]\sigma_{1}=2.3[/tex] represent the population standard deviation for Gibbs

[tex]\sigma_{2}=2.9[/tex] represent the sample standard deviation for the competitor

[tex]n_{1}=40[/tex] sample size for the group Gibbs

[tex]n_{2}=55[/tex] sample size for the group competitor

[tex]\alpha=0.05[/tex] Significance level provided

z would represent the statistic

Hypothesis to verify

We want to check if babies using the Gibbs brand gained less weight, the system of hypothesis would be:  

Null hypothesis:[tex]\mu_{1}-\mu_{2}=0[/tex]  

Alternative hypothesis:[tex]\mu_{1} - \mu_{2}< 0[/tex]  

The statistic would be given by:

[tex]z=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}[/tex] (1)  

Replacing the info given we got:

[tex]z=\frac{(7.6-8.1)-0}{\sqrt{\frac{2.3^2}{40}+\frac{2.9^2}{55}}}}=-0.936[/tex]  

The p value can be founded with this formula:

[tex]p_v =P(z<-0.936)=0.175[/tex]  

Since the p value is higher than the significance level provided of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean for the Gibbs brand is significantly lower than the true mean for the competitor

What would be the coordinates of the image if this pre-image is reflected across the x-axis?

A(-2, 2), (1, 1), (3, 1), (2, 4)
B(2,-2), (-1, 1), (-3,-1). (-2,-4)
C(-2, 2), (1, -1), (3, 1). (2,4)
D(-2,-2), (-1, 1), (-3, -1) (-2,-4)​

Answers

Answer:  C   (-2, 2), (1, -1), (3, 1). (2,4)

It will help to rotate the image so the x-axis is horizintal and the y-axis is vertical.

Step-by-step explanation:

Imagine the prefigure twirling on a parallel bar like a gymnast.

When it's up-side down the point that was at  (1,1) flips to (1. -1) and the point that was at  (3 -1) flips to (3, 1)

As you chech your choices, that knocks out most of the other possibilities.

But you should still verify the other cocorinates.

Hint: if the reflection is across the x-axis, the x values will be the same in the pre-image and the reflection, the y- values will change accorfing to their distance from the x-axis.

Simplify the radical below.
Square root 84
A. 221
B. 242
C. 4.21
D. 4.42
Pls no explanation will give you 20 points in in a hurry

Answers

the answer is B

Step-by-step explanation:

and I would love 20 points

Will get the brainiest answer for this problem involving a number line!

Answers

Answer:

61/1513/15

Step-by-step explanation:

The fill-in for the first box is found by counting spaces between 0 and 2/5. There are 6 of them.

__

Since 6 spaces = 2/5, the value of 1 space is 1/6 of 2/5. We must multiply 2/5 by 1/6 to find the value of 1 space:

  1 space = (2/5)(1/6) = 2/30 = 1/15

This is the number that goes in the second box.

__

To find the value of x, count all the spaces. There are 13, so the value of x is 13 times the value of 1 space:

  x = 13(1/15) = 13/15

This is the number that goes in the last box.

To measure the height of the cloud cover at an airport, a worker shines a spotlight upward at an angle 75° from the horizontal. an observer at a distance d = 560 m away measures the angle of elevation to the spot of light to be 45°. find the height h of the cloud cover,

Answers

Answer:

The height of the cloud cover is 441.66 meters

Step-by-step explanation:

Distance = 560 m

The height of the cloud cover = h meters

According to the diagram, the worker stands at point R,

Let RT = x

tan 45⁰ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{h}{x}[/tex]

therefore, 1 =  [tex]\frac{h}{x}[/tex], h = x

Then tan 75⁰ = [tex]\frac{h}{560-x}[/tex], substituting x = h, we have

3.732 = [tex]\frac{h}{560-h}[/tex]

3.732(560 - h) =  h

3.732 × 560 = 3.732h + h

2089.92 = 4.732h

h = 441.66 m

The height of the cloud cover is 228.62 meters

The given parameters are:

[tex]\mathbf{\alpha = 75^o}[/tex]

[tex]\mathbf{\theta = 45^o}[/tex]

[tex]\mathbf{d = 560m}[/tex]

See attachment for the image of the cloud cover.

From the attached image, we have the following sine ratios:

[tex]\mathbf{sin(75) = \frac hx}[/tex]

[tex]\mathbf{sin(45) = \frac h{560 - x}}[/tex]

Make h the subject in both equations

[tex]\mathbf{ h = xsin(75)}[/tex]

[tex]\mathbf{ h = (560 - x) sin(45)}[/tex]

So, we have:

[tex]\mathbf{ xsin(75) = (560 - x) sin(45)}[/tex]

Open brackets

[tex]\mathbf{ xsin(75) = 560sin(45) - x sin(45)}[/tex]

Collect like terms

[tex]\mathbf{ xsin(75) + x sin(45)= 560sin(45) }[/tex]

Evaluate sine 45 and 75

[tex]\mathbf{ 0.9659x + 0.7071x= 560 \times 0.7071}[/tex]

[tex]\mathbf{ 1.673x= 395.976}[/tex]

Divide both sides by 1.673

[tex]\mathbf{ x= 236.69}[/tex]

Recall that:

[tex]\mathbf{ h = xsin(75)}[/tex]

So, we have:

[tex]\mathbf{h = 236.69 \times 0.9659}[/tex]

[tex]\mathbf{h = 228.618871}[/tex]

Approximate

[tex]\mathbf{h = 228.62}[/tex]

Hence, the height of the cloud cover is 228.62 meters

Read more at:

https://brainly.com/question/16979479


For the inverse variation equation xy = k, what is the constant of variation, k, when x = 7 and y = 3?

Answers

Answer:

k=21

Step-by-step explanation:

x=7 X y=3 = 21

7 x 3 = 21

Answer:21

Step-by-step explanation:

xy=k

k=xy x=7 y=3

k=7 x 3

k=21

Subtracting by adding up 65-39

Answers

Answer:

26

Step-by-step explanation:

In order to subtract by adding up 65-39, we need to add -39 to the value of 65. This can be rewritten in this way;

65+(-39)

The equation above is similar to the one given because the product of a minus and a plus sign will still give us back a minus sign.

on solving;

65+(-39) = 26

Rewrite the percentage in the sentence below as a decimal.
The 20 overseas investors own 7.2% of the business.

Answers

Answer:

0.072

Step-by-step explanation:

Answer:0.072

Step-by-step explanation:

7.2% = 7.2/100

7.2 ➗ 100=0.072

Ms Davis is doing an activity with her statistic students where she gives them a 20 question multiple top choice test and they know none of the answers. Students need to guess on every question and each question has 5 possible choices, 1 of the which is correct.

What is the mean and standard deviation of the number of questions that each student gets correct?

Answers

Answer:

The mean and standard deviation of the number of questions that each student gets correct are 4 and 1.789 respectively.

Step-by-step explanation:

Let the random variable X be defined as the number of correct answers marked by a student.

It is provided that each question has 5 possible choices, 1 of the which is correct.

Then the probability of marking thee correct option is:

[tex]P(X)=\frac{1}{5}=0.20[/tex]

There are a total of n = 20 questions to be answered.

As the students does not the answer to any question, they would be guessing for each question. This implies that for a random question, all the five options has the equal probability of being correct and each of the five options can be correct independently from the other.

All these information above indicates that the random variable X follows a Binomial distribution with parameters n = 20 and p = 0.20.

The mean and standard deviation of a Binomial distribution are:

[tex]\mu=np\\\\\sigma=\sqrt{np(1-p)}[/tex]

Compute the mean and standard deviation of the random variable X as follows:

[tex]\mu=np=20\times 0.20=4\\\\\sigma=\sqrt{np(1-p)}=\sqrt{20\times 0.20\times(1-0.20)}=1.789[/tex]

Thus, the mean and standard deviation of the number of questions that each student gets correct are 4 and 1.789 respectively.

The mean will be "4" and the standard deviation will "1.789".

According to the question,

The probability of making 3 correct options will be:

→ [tex]P(X) = \frac{1}{5}[/tex]

            [tex]= 0.20[/tex]

Total number of questions,

n = 20

As we know,

The mean will be:

→ [tex]\mu = np[/tex]

By substituting the values, we get

     [tex]= 20\times 0.20[/tex]

     [tex]= 4[/tex]

and,

The standard deviation will be:

→ [tex]\sigma = \sqrt{np(1-p)}[/tex]

      [tex]= \sqrt{20\times 0.20\times (1-0.20)}[/tex]

      [tex]= 1.789[/tex]

Thus the responses above are correct.

Learn more about standard deviation here:

https://brainly.com/question/20896613

55 POINTS IF YOU GET RIGHT THEN GOATED AND BRAINIEST!!

Answers

Answer:

17 i would say it is D

18 i belive it is B

19 it is c

20 A

How many boys are there in an introductory geology course if 360 students are enrolled and there are five boys to every seven girls?

Answers

Answer:150 branliest

Step-by-step explanation:

Answer:

150

Step-by-step explanation:

360/(5+7)=30

30*5=150

If f(x)=9x+2, What is the value of the function when x=4?

If f(x)=9x+2, for what value of x is the value of the function 29?

Answers

Answer:

1) 38

2) 3

Step-by-step explanation:

f(x)=36+2

f(x)=38

29=9x+2

27=9x

x=3

Question: What is the value of the function at x=−2?

Answer: y=2

Step-by-step explanation: I took the test.

*THIS IS THE CORRECT ANSWER. PLEASE DON'T ANSWER 3. IT IS WRONG!*

Write parametric equations of the line 2x - y = 3.
a. X = 1, y = 2t - 2
c.
X = 1, y = 3t-2
b. X= 1, y = 2t-3
d.
1
1
X = 1,y= =
2
1.9 -
3
Please select the best answer from the choices provided
A
OB
С
OD

Answers

or anything else please send me a text c because

The corresponding sides of ΔABC and ΔDEF have equal lengths. The area of ΔABC is 4 square units, and the longest side of ΔDEF is 5 units long. What is the area of ΔDEF?

Answers

Answer:

  4 square units

Step-by-step explanation:

If corresponding sides have equal lengths, the triangles are congruent by the SSS postulate. They must have equal areas: 4 square units.

ΔDEF has an area of 4 square units.

Answer:

if the corresponding sides are equal the 2 triangles are congruent  ( by SSS) so their areas are the same.

So area of triangle DEF = 4 sq units

Step-by-step explanation:

What is the volume of a rectangular prism with the following dimensions?



h = 5 ft, w = 5 ft, l = 10 ft

20 ft 3
500 ft 3
250 ft 3
35 ft 3

Answers

Answer:

250

Step-by-step explanation:

V = LWH

5 * 5 * 10 = 250

(5+2×3)−4+(5x5) ? Highly appreciate it. :)

Answers

Answer:

32

Step-by-step explanation:

Answer: 32

Step-by-step explanation:

c. two hundred thirty-one and five tenths - in decimal standard form​

Answers

Answer:

231.5

five tenths = 0.5

Standard form of a decimal 231.5

Really need help on this. I keep gettin it wrong please help!!!

Answers

Answer:

1436.76 m³

Step-by-step explanation:

Volume of sphere= 4/3 π r ³

V= 4/3(3.14)(7)³

V=4/3(3.14)(343)

V= 4310.26 / 3

V= 1436.76 m³

Daniel believes that people perform better in the barbell curl, on average, if they are encouraged by a coach. He recruited 29 subjects to participate in an experiment and randomly assigned them into two groups. Daniel gave one group verbal encouragement during the exercise and was quiet during the exercise for the other group. He recorded the total number of barbell curls each subject was able to complete before setting the bar down.

Explain the purpose of random assignment in this experiment.

Answers

Answer:

Define two roughly identical sets.

Reduce the chance of bias.

Step-by-step explanation:

In this experiment, Daniel performs a random assignment in order to stablish two separate groups with roughly equivalent ability to do barbell curls. Two different treatments (verbal encouragement and silence) are then applied in order to verify for a cause and effect relationship. If the groups were not randomly assigned, then the experiment could be biased.

What parallelogram has a base of 2 units and a height of 4 units

Answers

Answer:

C

Step-by-step explanation:

The parallelogram in C has a base of 2 units and a height o 4 units.

Carpetland carpet installers incur an average cost of $300 for each carpet installed. Joan Chin, the firm’s vice president, proposes a new procedure for installations, which she hopes will be more efficient. Joan plans to run a trial and hopes that the results of a trial period will enable her to conclude with a level of significance of 0.05 that the new procedure reduces the average cost to install a carpet. If Joan's hypothesis test results in a Type II error, what would this mean?

Answers

Answer:

A Type II error happens when the null hypothesis failed to be rejected, although it is false and the alternative hypothesis is true.

In this context, would be that the test does not give enough evidence to support the claim that the new procedure reduces the average cost, although it really does reduces it.

The new procedure is effective, but the sample does not give enough evidence.

Step-by-step explanation:

Which mixes number is equivalent to the improper fraction 4/3

Answers

Answer:

1 1/3

Step-by-step explanation:

take the denominator and times it to the mixed number.

so 3*1 = 3

then add the numerator to that, so

3 + 1 = 4

making it, 4/3

add 5 1/2 kg to 450g​

Answers

1kg = 1000g

51/2 kg= 51/2×1000=51×500=25500g

25500g+450g= 25950g

Answer:

[tex]5950g[/tex]

Step-by-step explanation:

[tex]5 \frac{1}{2} kg \\ = 5kg \: 500g \\ = 5500g[/tex]

Now let's add.

[tex] \: \: \: \: \: \: 5500g \\ + \: \: \: \: 450g \\ =5950 g[/tex]

So the correct answer is,

[tex] = 5950g = 5kg \: 950g[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

What is the solution to the system of equations?

3 x + 10 y = negative 47. 5 x minus 7 y = 40.
(1, –5)
(1, 5)
(–1, –5)
(–1, 5)

Answers

Answer:

  (1, –5)

Step-by-step explanation:

It is relatively easy to try the offered solutions to see what works.

(1, -5)

  3(1) +10(-5) = -47 . . . true

  5(1) -7(-5) = 40 . . . true

(1, -5) is the solution

_____

As a check, you can try some of the other choices:

(1, 5)

  3(1) +10(5) ≠ -47

(-1, -5)

  3(-1) +10(-5) ≠ -47

(-1, 5)

  3(-1) +10(5) ≠ -47

None of the other choices works in the first equation, so they're not the solution.

Answer:

(1,-5)

Step-by-step explanation:

1)get desmos

2)put in numbers

3)where they intersect is the answer.

easy as pie... oh wait pie ain't easy...

easy as ramen

A bag contains 10 Yellow, 4 Green and 7 Blue marbles. Find the following probabilies.
P(blue)

Answers

Answer:

1/3

Step-by-step explanation:

The total number of marbles

10+4+7 = 21

P(blue) = blue marbles / total marbles

            = 7 / 21

            = 1/3

You need to be taller than 48" to ride the roller coaster. Which of the following inequalities shows the height Susan has to be to ride the roller coaster.

h < 48"

h > 48"

h ≤ 48"

h ≥ 48"

Answers

Answer:

> 48"

Step-by-step explanation:

> represents greater than 48"

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Consider a portfolio manager with a $20,500,000 equity portfolio under management. The manager wishes to hedge against a decline in share values using stock index futures. Currently a stock index future is priced at 1250 and has a multiplier of 250. The portfolio beta is 1.25. Calculate the number of contracts required to hedge the risk exposure and indicate whether the manager should be short or long. Marias height while jumping on a trampoline can be given by the equation: -16^2+16x+5 If a demand curve shown above shift to the left then the________.. 56. Respond in a paragraph with complete sentences.(16 pointChoose one literary selection from this semester in which you think the setting has a greatimpact on the work. In a full paragraph, name the work, describe the setting, and explain whyit is so important to the overall story or poem.*I REALLY NEED HELP ON THIS QUESTION PLEASE HELP ME* :( Block A, with a mass of 4 kg, is moving with a speed of 2 m/s while Block B, with a mass of 8.4 kg, is moving in the opposite direction with a speed of 6.1 m/s. The center of mass of the two block system is moving with a velocity of ____ m/s. Round your answer to the nearest tenth. Assume Block A is moving in the positive direction. Mr. Mole's burrow lies 5 meters below the ground. He started digging his way deeper into the ground, descending 3 meters each minute.Graph the relationship between Mr. Mole's elevation relative to the ground (in meters) and time (in minutes). Which one has higher ecosystem diversity, rain forest or desert? Really need help on this. I keep gettin it wrong please help!!! Can you answer this science question for me please? Employees at a manufacturing plant have seen productionrates change by approximately 105% annually. In contrast,the graph shows the change in the average annual wagesof the employeesWhich statement accurately compares the annual changein production to the annual change in average salary?50.00050.0000 The annual changes cannot be compared because theinitial production value is unknown.The annual change in production will, at some point,exceed the annual change in average salaryThe annual change in production increases at a slowerrate, 5% per year, than the annual increase in theaverage salary, $500 per year.The annual change in production increases at a slowerrate, 105% per year, than the annual increase in averagesalary, $500 per year4030.00020.00010.000 Write the cubic term for the Taylor series expansion of f(x) = sin(x) at c = pi/4I did the work, can you please check for me whether my work is right? Find the area of the rhombus. What impact does the loss of the sphere have on the plot? The First Men in the MoonA. Mr.Bedford will not be able to return to the moon. B. All of the gold has been lost with the sphere. C. Mr.Bedford must make a new sphere.D. Other people will discover how to make Mr.Cavorite. Find the area of the trapezoid If you made 6 moles of NO2 how many grams of N2 did you use? What is the solution to the system of equations?3 x + 10 y = negative 47. 5 x minus 7 y = 40.(1, 5)(1, 5)(1, 5)(1, 5) Which mixes number is equivalent to the improper fraction 4/3 How did the first railroad cars move on the rails?wind powerhorsesgasoline enginessteam power If f(x)=9x+2, What is the value of the function when x=4?If f(x)=9x+2, for what value of x is the value of the function 29? You need to be taller than 48" to ride the roller coaster. Which of the following inequalities shows the height Susan has to be to ride the roller coaster.h < 48"h > 48"h 48"h 48"